First order reliability method on soil strength parameters estimation and stability analysis

Abstract

The application of the first order reliability method (FORM) on the estimation of soil strength parameters and on the probabilistic analysis of slope stability problems is examined. Typical slope stability problems use the bi-parametric Mohr - Coulomb failure criterion and modern codes of practice (e.g. EC7) require some statistical measures for analyses purposes, either deterministic or probabilistic. Statistical approaches for the estimation of the measures of (a) the best estimate and uncertainty of these parameters (used in probabilistic analyses) and (b) their characteristic value (used in deterministic analyses) are presented herein. The uncertainty is estimated either by direct statistical methods or by application of the FORM, a methodology for uncertainty (via error propagation) calculation. Equations of uncertainty are derived for the direct shear- and the typical triaxial-test. An application of the FORM to the planar failure limit equilibrium problem is presented, which can be adjusted to the slices’ method. The reliability check with respect to the safety margin is preferable as it reduces the non-linearity effects, while the influence of cohesion uncertainty is more critical. A sensitivity check with regards to the uncertainties of soil parameter is recommended for probabilistic analyses.